Automatically setting the rendering frame range in compositing
Turns out I just wasn't accessing the right object type. The movie clip node contains a clip parameter, which contains the data I needed. The frame end range can then be set like this:

frameCount = bpy.data.scenes['Scene'].node_tree.nodes["MovieClip"].clip.frame_duration
bpy.context.scene.frame_end = frameCount


Full specification of the MovieClip datatype can be found here